(1 point) State sales tax $y$ is directly proportional to retail price $x$. An item that sells for 186 dollars has a sales tax of 10.22 dollars. Find a mathematical model that gives the amount of sales tax $y$ in terms of the retail price $x$. Your answer is $y=$ What is the sales tax on a 340 dollars purchase. Your answer is:

Step 1 ：The problem states that the sales tax $y$ is directly proportional to the retail price $x$. This means that the relationship between $y$ and $x$ can be expressed as $y = kx$, where $k$ is the constant of proportionality.

Step 2 ：We can find the value of $k$ by substituting the given values of $y$ and $x$ into the equation. Given that an item that sells for 186 dollars has a sales tax of 10.22 dollars, we substitute these values into the equation to get $10.22 = k \times 186$.

Step 3 ：Solving for $k$, we get $k = \frac{10.22}{186} = 0.054946236559139786$.

Step 4 ：Now that we have the value of $k$, we can use it to find the sales tax on a 340 dollars purchase. Substituting $x = 340$ into the equation $y = kx$, we get $y = 0.054946236559139786 \times 340 = 18.68172043010753$.

Step 5 ：Rounding to the nearest cent, the sales tax on a 340 dollars purchase is \(\boxed{18.68}\) dollars.